Stat 401B
Lab 3
Due September 19, 2006
1
A study was done to see if Body Fat (as a percentage of total mass) could be predicted
from a simple measurement, Thigh Circumference (cm). Twenty individuals, randomly
selected from the local population, agree to participate. For each individual, Body Fat
(%) is determined by water displacement. Thigh Circumference is measured at a specified
distance above the knee. Below are the twenty pairs of measurements.
Thigh (cm)
43.1
49.8
51.9
54.3
42.2
53.9
58.5
52.1
49.9
53.5
Body Fat (%)
11.9
22.8
18.7
20.1
12.9
21.7
27.1
25.4
21.3
19.3
Thigh (cm)
56.6
56.7
46.5
44.2
42.7
54.4
55.3
58.6
48.2
51.0
Body Fat (%)
25.4
27.2
11.7
17.8
12.8
23.9
22.6
25.4
14.8
21.1
1. Use JMP’s Fit Y by X to obtain a plot of Body Fat versus Thigh Circumference.
Describe the general relationship between the two variables.
2. Report the least squares equation of the line.
3. Give an interpretation of the slope within the context of the problem.
4. Give the value of R2 and an interpretation of this value within the context of the
problem.
5. Give the value of SY |X , the estimate of the error standard deviation.
6. Test the hypothesis that the slope parameter, β1 is zero against the alternative that it
is not zero.
7. Construct a 95% confidence interval for the slope parameter, β1 . Does this agree with
the results of your test in (d)? Explain briefly.
8. Obtain a plot of residuals versus Thigh Circumference. Are there any unusual patterns
or points? If so, comment on the pattern and/or indicate the unusual points.
9. Use Confid Curves Indiv to put prediction bands on your plot of the data. Do any
of the points fall outside the prediction bands? If so, indicate these points.
10. Save Predicteds and Save Residuals. What is the predicted Body Fat for a Thigh
Circumference of 51 cm? What is the residual associated with this prediction?
11. Use Basic Stats, Distribution to analyze the residuals. Based on this analysis, and
any plots from the previous analysis, comment on each of the conditions necessary for
regression analysis.
Turn in the output of Fit Y by X and the analysis of the residuals with the answers to the
questions.